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(x*log(1+1/x))^(x^5)
Derivada de la función/ 1+1/x/ x*log/ (x^5)/ (x*log(1+1/x))^(x^5)

Derivada de (x*log(1+1/x))^(x^5)

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
              / 5\
              \x /
/     /    1\\    
|x*log|1 + -||    
\     \    x//
(xlog⁡(1+1x))x5\left(x \log{\left(1 + \frac{1}{x} \right)}\right)^{x^{5}} 
(x*log(1 + 1/x))^(x^5)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(x5)+1)(x5)x5\left(\log{\left(x^{5} \right)} + 1\right) \left(x^{5}\right)^{x^{5}}

Respuesta:

(log⁡(x5)+1)(x5)x5\left(\log{\left(x^{5} \right)} + 1\right) \left(x^{5}\right)^{x^{5}}

Gráfica
02468-8-6-4-2-10102.5-2.5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                   /                          4 /      1          /    1\\\
                   |                         x *|- --------- + log|1 + -|||
              / 5\ |                            |    /    1\      \    x/||
              \x / |                            |  x*|1 + -|             ||
/     /    1\\     |   4    /     /    1\\      \    \    x/             /|
|x*log|1 + -||    *|5*x *log|x*log|1 + -|| + -----------------------------|
\     \    x//     |        \     \    x//                /    1\         |
                   |                                   log|1 + -|         |
                   \                                      \    x/         /
(xlog⁡(1+1x))x5(x4(log⁡(1+1x)−1x(1+1x))log⁡(1+1x)+5x4log⁡(xlog⁡(1+1x)))\left(x \log{\left(1 + \frac{1}{x} \right)}\right)^{x^{5}} \left(\frac{x^{4} \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\log{\left(1 + \frac{1}{x} \right)}} + 5 x^{4} \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)}\right)
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Segunda derivada [src] 
                     /                                                   2                                                                                                                 \
                     |   /                            1          /    1\\                                                       2 /      1          /    1\\     /      1          /    1\\|
                     |   |                      - --------- + log|1 + -||                                                    9*x *|- --------- + log|1 + -||   x*|- --------- + log|1 + -|||
                / 5\ |   |                          /    1\      \    x/|                                                         |    /    1\      \    x/|     |    /    1\      \    x/||
                \x / |   |                        x*|1 + -|             |                                                         |  x*|1 + -|             |     |  x*|1 + -|             ||
  /     /    1\\     | 7 |     /     /    1\\       \    x/             |             1                2    /     /    1\\        \    \    x/             /     \    \    x/             /|
x*|x*log|1 + -||    *|x *|5*log|x*log|1 + -|| + ------------------------|  - ------------------- + 20*x *log|x*log|1 + -|| + ------------------------------- + ----------------------------|
  \     \    x//     |   |     \     \    x//             /    1\       |           2                       \     \    x//                 /    1\                 /    1\    2/    1\     |
                     |   |                             log|1 + -|       |    /    1\     /    1\                                        log|1 + -|                 |1 + -|*log |1 + -|     |
                     |   \                                \    x/       /    |1 + -| *log|1 + -|                                           \    x/                 \    x/     \    x/     |
                     \                                                       \    x/     \    x/                                                                                           /
x(xlog⁡(1+1x))x5(x7(log⁡(1+1x)−1x(1+1x)log⁡(1+1x)+5log⁡(xlog⁡(1+1x)))2+9x2(log⁡(1+1x)−1x(1+1x))log⁡(1+1x)+20x2log⁡(xlog⁡(1+1x))+x(log⁡(1+1x)−1x(1+1x))(1+1x)log⁡(1+1x)2−1(1+1x)2log⁡(1+1x))x \left(x \log{\left(1 + \frac{1}{x} \right)}\right)^{x^{5}} \left(x^{7} \left(\frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\log{\left(1 + \frac{1}{x} \right)}} + 5 \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)}\right)^{2} + \frac{9 x^{2} \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\log{\left(1 + \frac{1}{x} \right)}} + 20 x^{2} \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)} + \frac{x \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right) \log{\left(1 + \frac{1}{x} \right)}^{2}} - \frac{1}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}}\right)
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3-я производная [src] 
                   /                                                    3                                                                                                                                                                                                                                                                                                                                                                                                           \
                   |    /                            1          /    1\\                                                          1          /    1\                                                      /      1          /    1\\        /                            1          /    1\\ /                                                     2 /      1          /    1\\     /      1          /    1\\\       2 /      1          /    1\\        /      1          /    1\\|
                   |    |                      - --------- + log|1 + -||                                                    - --------- + log|1 + -|                                                    2*|- --------- + log|1 + -||        |                      - --------- + log|1 + -|| |                                                  9*x *|- --------- + log|1 + -||   x*|- --------- + log|1 + -|||   47*x *|- --------- + log|1 + -||   11*x*|- --------- + log|1 + -|||
              / 5\ |    |                          /    1\      \    x/|                                                        /    1\      \    x/                                                      |    /    1\      \    x/|        |                          /    1\      \    x/| |                                                       |    /    1\      \    x/|     |    /    1\      \    x/||         |    /    1\      \    x/|        |    /    1\      \    x/||
              \x / |    |                        x*|1 + -|             |                                                      x*|1 + -|                                                                   |  x*|1 + -|             |        |                        x*|1 + -|             | |                                                       |  x*|1 + -|             |     |  x*|1 + -|             ||         |  x*|1 + -|             |        |  x*|1 + -|             ||
/     /    1\\     | 12 |     /     /    1\\       \    x/             |             10               2    /     /    1\\       \    x/                          2                       2                \    \    x/             /      5 |     /     /    1\\       \    x/             | |           1                2    /     /    1\\        \    \    x/             /     \    \    x/             /|         \    \    x/             /        \    \    x/             /|
|x*log|1 + -||    *|x  *|5*log|x*log|1 + -|| + ------------------------|  - ------------------- + 60*x *log|x*log|1 + -|| + ------------------------ - --------------------- - ---------------------- + ---------------------------- + 3*x *|5*log|x*log|1 + -|| + ------------------------|*|- ------------------- + 20*x *log|x*log|1 + -|| + ------------------------------- + ----------------------------| + -------------------------------- + -------------------------------|
\     \    x//     |    |     \     \    x//             /    1\       |           2                       \     \    x//            2                          3                       3                          2                        |     \     \    x//             /    1\       | |         2                       \     \    x//                 /    1\                 /    1\    2/    1\     |                 /    1\                    /    1\    2/    1\      |
                   |    |                             log|1 + -|       |    /    1\     /    1\                               /    1\     2/    1\       /    1\     /    1\     /    1\     2/    1\       /    1\     3/    1\            |                             log|1 + -|       | |  /    1\     /    1\                                        log|1 + -|                 |1 + -|*log |1 + -|     |              log|1 + -|                    |1 + -|*log |1 + -|      |
                   |    \                                \    x/       /    |1 + -| *log|1 + -|                               |1 + -| *log |1 + -|     x*|1 + -| *log|1 + -|   x*|1 + -| *log |1 + -|       |1 + -| *log |1 + -|            \                                \    x/       / |  |1 + -| *log|1 + -|                                           \    x/                 \    x/     \    x/     |                 \    x/                    \    x/     \    x/      |
                   \                                                        \    x/     \    x/                               \    x/      \    x/       \    x/     \    x/     \    x/      \    x/       \    x/      \    x/                                                             \  \    x/     \    x/                                                                                           /                                                                     /
(xlog⁡(1+1x))x5(x12(log⁡(1+1x)−1x(1+1x)log⁡(1+1x)+5log⁡(xlog⁡(1+1x)))3+3x5(log⁡(1+1x)−1x(1+1x)log⁡(1+1x)+5log⁡(xlog⁡(1+1x)))(9x2(log⁡(1+1x)−1x(1+1x))log⁡(1+1x)+20x2log⁡(xlog⁡(1+1x))+x(log⁡(1+1x)−1x(1+1x))(1+1x)log⁡(1+1x)2−1(1+1x)2log⁡(1+1x))+47x2(log⁡(1+1x)−1x(1+1x))log⁡(1+1x)+60x2log⁡(xlog⁡(1+1x))+11x(log⁡(1+1x)−1x(1+1x))(1+1x)log⁡(1+1x)2+log⁡(1+1x)−1x(1+1x)(1+1x)2log⁡(1+1x)2+2(log⁡(1+1x)−1x(1+1x))(1+1x)2log⁡(1+1x)3−10(1+1x)2log⁡(1+1x)−2x(1+1x)3log⁡(1+1x)−2x(1+1x)3log⁡(1+1x)2)\left(x \log{\left(1 + \frac{1}{x} \right)}\right)^{x^{5}} \left(x^{12} \left(\frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\log{\left(1 + \frac{1}{x} \right)}} + 5 \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)}\right)^{3} + 3 x^{5} \left(\frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\log{\left(1 + \frac{1}{x} \right)}} + 5 \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)}\right) \left(\frac{9 x^{2} \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\log{\left(1 + \frac{1}{x} \right)}} + 20 x^{2} \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)} + \frac{x \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right) \log{\left(1 + \frac{1}{x} \right)}^{2}} - \frac{1}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}}\right) + \frac{47 x^{2} \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\log{\left(1 + \frac{1}{x} \right)}} + 60 x^{2} \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)} + \frac{11 x \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right) \log{\left(1 + \frac{1}{x} \right)}^{2}} + \frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}^{2}} + \frac{2 \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}^{3}} - \frac{10}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}} - \frac{2}{x \left(1 + \frac{1}{x}\right)^{3} \log{\left(1 + \frac{1}{x} \right)}} - \frac{2}{x \left(1 + \frac{1}{x}\right)^{3} \log{\left(1 + \frac{1}{x} \right)}^{2}}\right)
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Tercera derivada [src] 
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                   |    /                            1          /    1\\                                                          1          /    1\                                                      /      1          /    1\\        /                            1          /    1\\ /                                                     2 /      1          /    1\\     /      1          /    1\\\       2 /      1          /    1\\        /      1          /    1\\|
                   |    |                      - --------- + log|1 + -||                                                    - --------- + log|1 + -|                                                    2*|- --------- + log|1 + -||        |                      - --------- + log|1 + -|| |                                                  9*x *|- --------- + log|1 + -||   x*|- --------- + log|1 + -|||   47*x *|- --------- + log|1 + -||   11*x*|- --------- + log|1 + -|||
              / 5\ |    |                          /    1\      \    x/|                                                        /    1\      \    x/                                                      |    /    1\      \    x/|        |                          /    1\      \    x/| |                                                       |    /    1\      \    x/|     |    /    1\      \    x/||         |    /    1\      \    x/|        |    /    1\      \    x/||
              \x / |    |                        x*|1 + -|             |                                                      x*|1 + -|                                                                   |  x*|1 + -|             |        |                        x*|1 + -|             | |                                                       |  x*|1 + -|             |     |  x*|1 + -|             ||         |  x*|1 + -|             |        |  x*|1 + -|             ||
/     /    1\\     | 12 |     /     /    1\\       \    x/             |             10               2    /     /    1\\       \    x/                          2                       2                \    \    x/             /      5 |     /     /    1\\       \    x/             | |           1                2    /     /    1\\        \    \    x/             /     \    \    x/             /|         \    \    x/             /        \    \    x/             /|
|x*log|1 + -||    *|x  *|5*log|x*log|1 + -|| + ------------------------|  - ------------------- + 60*x *log|x*log|1 + -|| + ------------------------ - --------------------- - ---------------------- + ---------------------------- + 3*x *|5*log|x*log|1 + -|| + ------------------------|*|- ------------------- + 20*x *log|x*log|1 + -|| + ------------------------------- + ----------------------------| + -------------------------------- + -------------------------------|
\     \    x//     |    |     \     \    x//             /    1\       |           2                       \     \    x//            2                          3                       3                          2                        |     \     \    x//             /    1\       | |         2                       \     \    x//                 /    1\                 /    1\    2/    1\     |                 /    1\                    /    1\    2/    1\      |
                   |    |                             log|1 + -|       |    /    1\     /    1\                               /    1\     2/    1\       /    1\     /    1\     /    1\     2/    1\       /    1\     3/    1\            |                             log|1 + -|       | |  /    1\     /    1\                                        log|1 + -|                 |1 + -|*log |1 + -|     |              log|1 + -|                    |1 + -|*log |1 + -|      |
                   |    \                                \    x/       /    |1 + -| *log|1 + -|                               |1 + -| *log |1 + -|     x*|1 + -| *log|1 + -|   x*|1 + -| *log |1 + -|       |1 + -| *log |1 + -|            \                                \    x/       / |  |1 + -| *log|1 + -|                                           \    x/                 \    x/     \    x/     |                 \    x/                    \    x/     \    x/      |
                   \                                                        \    x/     \    x/                               \    x/      \    x/       \    x/     \    x/     \    x/      \    x/       \    x/      \    x/                                                             \  \    x/     \    x/                                                                                           /                                                                     /
(xlog⁡(1+1x))x5(x12(log⁡(1+1x)−1x(1+1x)log⁡(1+1x)+5log⁡(xlog⁡(1+1x)))3+3x5(log⁡(1+1x)−1x(1+1x)log⁡(1+1x)+5log⁡(xlog⁡(1+1x)))(9x2(log⁡(1+1x)−1x(1+1x))log⁡(1+1x)+20x2log⁡(xlog⁡(1+1x))+x(log⁡(1+1x)−1x(1+1x))(1+1x)log⁡(1+1x)2−1(1+1x)2log⁡(1+1x))+47x2(log⁡(1+1x)−1x(1+1x))log⁡(1+1x)+60x2log⁡(xlog⁡(1+1x))+11x(log⁡(1+1x)−1x(1+1x))(1+1x)log⁡(1+1x)2+log⁡(1+1x)−1x(1+1x)(1+1x)2log⁡(1+1x)2+2(log⁡(1+1x)−1x(1+1x))(1+1x)2log⁡(1+1x)3−10(1+1x)2log⁡(1+1x)−2x(1+1x)3log⁡(1+1x)−2x(1+1x)3log⁡(1+1x)2)\left(x \log{\left(1 + \frac{1}{x} \right)}\right)^{x^{5}} \left(x^{12} \left(\frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\log{\left(1 + \frac{1}{x} \right)}} + 5 \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)}\right)^{3} + 3 x^{5} \left(\frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\log{\left(1 + \frac{1}{x} \right)}} + 5 \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)}\right) \left(\frac{9 x^{2} \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\log{\left(1 + \frac{1}{x} \right)}} + 20 x^{2} \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)} + \frac{x \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right) \log{\left(1 + \frac{1}{x} \right)}^{2}} - \frac{1}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}}\right) + \frac{47 x^{2} \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\log{\left(1 + \frac{1}{x} \right)}} + 60 x^{2} \log{\left(x \log{\left(1 + \frac{1}{x} \right)} \right)} + \frac{11 x \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right) \log{\left(1 + \frac{1}{x} \right)}^{2}} + \frac{\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}^{2}} + \frac{2 \left(\log{\left(1 + \frac{1}{x} \right)} - \frac{1}{x \left(1 + \frac{1}{x}\right)}\right)}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}^{3}} - \frac{10}{\left(1 + \frac{1}{x}\right)^{2} \log{\left(1 + \frac{1}{x} \right)}} - \frac{2}{x \left(1 + \frac{1}{x}\right)^{3} \log{\left(1 + \frac{1}{x} \right)}} - \frac{2}{x \left(1 + \frac{1}{x}\right)^{3} \log{\left(1 + \frac{1}{x} \right)}^{2}}\right)
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Gráfico
Derivada de (x*log(1+1/x))^(x^5)
    © Sr Examen – Калькулятор